Not a topic I've studied in particular detail but Sayyid Qutb wrote about his outrage as an Egyptian being denied entry to a segregated movie theater in Greeley, Colorado. When they protested that they were Egyptian and not black the theater owner relented and apologized but Qutb insisted that they not see the movie at all because of the offense. Qutb himself could be quite racist towards African-Americans, on the other hand.

I am not at all a scholar of American history, and really not the best person to answer this question.

I think the important thing to keep in mind is that race is a social construct. That is to say, while there are obvious differences between races in terms of how we look, what our skin colors are, what our hair texture is, the meaningfulness of those differences have a lot to do with social context. The case of Arabs in America is a really good example of this.

During much of the 19th century, Arabs were seen as not white. Or rather, like Greeks, Italians, Armenians etc they were seen as sort of white. White in some contexts, and not white in others. These groups had a tenuous whiteness. In the post-war period, cultural differences faded away, and Arabs became completely white. We think of Steve Jobs and Ralph Nader as white even though they are of Arab ancestry. Since 9/11 and recent acts of terrorism, Arabs (or at least Muslim Arabs) have lost a lot of their status as white people. Even though the genetics stayed the same, the way in which white people are perceived has changed noticably.

So, after my really long preface, let me actually answer your question. Generally speaking, Arab children attended white schools. In terms of most legal issues, they were considered white. They often faced discrimination. There are several documented examples of Arabs getting lynched, or almost lynched. Moreover, most became itinerant peddlers, selling food and other cheap items to black sharecroppers. They usually chose to work for themselves because they would face severe employment discrimination otherwise. There were limits on where they could live, although this depended a lot on the particular city or county. But as time went on, as the children of the first generation became more Americanized, Arabs became seen as more white. All the examples of discrimination I read about are from the 1880. I see little in 1960 against the grandchildren.

It's important to keep in mind race and racism are flexible concepts. Also, once again, this is a time period where my knowledge is limited at best.

Most likely not. I believe Asian Indians attempted to immigrate to North America and tried the legal route claiming Caucasian origin, but were denied.